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Example convolution

In some cases, however, we can in essence deconvolute. This special situation is considered at the end of Chapter 14 and is illustrated with an example there. Example 11.3 illustrates convolution Example 14.4 illustrates deconvolution. [Pg.272]

Another convoluted example is similar to the analysis of 26. Cyclic alkane 27 could be named l,l-dibromo-3-ethyl-4-methylcyclopentane, l,l-dibromo-4-ethyl-3-methylcyclopentane, 3,3-dibromo-l-ethyl-5-methylcyclopentane, 4,4-dibromo-l-ethyl-2-methylcyclopentane, 3,3-dibromo-5-ethyl- 1-methylcyclopentane, or 4,4-dibromo-2-ethyl-l-methylcyclopentane. The lowest combination of numbers is either l,l-dibromo-3-ethyl-4-methylcyclopentane or l,l-dibromo-4-ethyl-3-methylcyclopentane, but this choice leads to another dilemma because it coidd be 3-ethyl-4-methyl or 4-ethyl-3-methyl. To distinguish the latter, rely... [Pg.109]

Equation (Bl.8.6) assumes that all unit cells really are identical and that the atoms are fixed hi their equilibrium positions. In real crystals at finite temperatures, however, atoms oscillate about their mean positions and also may be displaced from their average positions because of, for example, chemical inlioniogeneity. The effect of this is, to a first approximation, to modify the atomic scattering factor by a convolution of p(r) with a trivariate Gaussian density function, resulting in the multiplication ofy ([Pg.1366]

Figure Bl.19.19. Examples of inaccessible features in AFM imaging. L corresponds to the AFM tip. The dotted curves show the image that is recorded in the case of (a) depressions on the underside of an object and (b) mounds on the top surface of an object. M- L andMoi correspond to convolutions of the surface features with the tip shape. (Taken from [ ], figure 2.)... Figure Bl.19.19. Examples of inaccessible features in AFM imaging. L corresponds to the AFM tip. The dotted curves show the image that is recorded in the case of (a) depressions on the underside of an object and (b) mounds on the top surface of an object. M- L andMoi correspond to convolutions of the surface features with the tip shape. (Taken from [ ], figure 2.)...
Patent documents differ from journal Hterature in several ways. First of all, they are legal documents whose disclosures support one or more claims that define an area of property rights. The language in patent documents can therefore be quite convoluted "patentese" as the appHcant strives to achieve the broadest possible scope of coverage. Examples provided in patents may never have happened. Based on the appHcant s understanding of the technical... [Pg.45]

Due to the convoluted mass and depth scales present in an RBS spectrum, it may not be possible to accurately describe an unknown sample using a single RBS spectrum. For example. Figure 4a is an RBS spectrum acquired at a backscattering angle of 160° from a sample implanted with 2.50 x 10 atoms/cm of As at a depth of approximately 140 nm. If this were a totally unknown sample it would not be possible to determine positively the mass and depth of the implanted species from this spectrum alone, since the peak in the RBS spectrum also could have been caused by a heavier element at greater depth, such as Sb at 450 nm, or Mo at 330 nm, or by a... [Pg.482]

The conversion of radiated power (P in watts) to luminous flux (F in lumens) is achieved by considering the variation with wavelength of the human eye s photopie response. Then the spectral power from the source (PA in, lor example, W/nnt) is convoluted with the relative spectral response of the eye (V tabulated by the CIE) according to ... [Pg.550]

A typical example at the other extreme where a de-convolution technique would be useless is given in figure 10. [Pg.276]

A series of measurements in which the pump wavelength is varied reveal that at some energies the oscillations predominate for times beyond lOps, whilst at others the decay of population by curve-crossing wins out within 400 fs or so. The time resolution of the experiment is in this example is determined by the convolution of the two laser pulse widths, here about 125fs. [Pg.11]

In many macroscopic systems, the massive behavior is a convoluted answer to many microscopic features of the system. For example, the catalysis of the electrooxidation of an organic molecule may be generated by some local arrangement of atoms on a catalyst, defined at the atomic level. If some hypotheses are available to explain the enhancement of the reaction, this can be checked by inserting these hypotheses in the model. In a first approximation, a qualitative explanation is often sought. If this is... [Pg.661]

If X (0 and Xjit) are the input and output functions in the time domain (for example, the contents in the reservoir and in the plasma compartment), then XJj) is the convolution of Xj(r) with G(t), the inverse Laplace transform of the transfer function between input and output ... [Pg.489]

By way of illustration the spectrometry example is worked out. Two functions are involved in the process, the signal/(X,) and the convolution function h(k). Both functions should be measured in the same domain and should be digitized with the same interval and at the same r-values (in spectrometry X-values). Let us furthermore assume that the spectrum/(A,) and convolution function h(k) have a simple triangular shape but with a different half-height width. [Pg.531]

From the convolution theorem it follows that the convolution of the two triangles in our example can also be calculated in the Fourier domain, according to the following scheme ... [Pg.533]

Here we must introduce a complication in the structures of cellular compartments. We have treated the small bacterial cells as one aqueous phase, the cytoplasm, within one containing membrane. Now there are many examples of the membrane inside the wall as a very convoluted structure with cristae reaching far... [Pg.219]

In the practice of solid-state bioEPR, a Lorentzian line shape will be observed at relatively high temperatures and its width as a function of temperature can be used to deduce relaxation rates, while a Gaussian line will be observed at relatively low temperatures and its linewidth contains information on the distributed nature of the system. What exactly is high and low temperature, of course, depends on the system for the example of low-spin cytochrome a in Figure 4.2, a Lorentzian line will be observed at T = 80°C, and a Gaussian line will be found at T 20°C, while at T 50°C a mixture (a convolution) of the two distributions will be detected. [Pg.60]

It is important to keep in mind that demands occur on the time line. If a reasonable minimal time interval is chosen, it is in many cases justified to consider the demands in these intervals as independent and identically distributed random variables. This means for example that the demand per week is the iterated convolution of the daily demand. A large customer base is a good indicator of independent random demand in different time intervals. [Pg.114]


See other pages where Example convolution is mentioned: [Pg.1974]    [Pg.549]    [Pg.74]    [Pg.75]    [Pg.56]    [Pg.94]    [Pg.483]    [Pg.878]    [Pg.961]    [Pg.274]    [Pg.274]    [Pg.556]    [Pg.153]    [Pg.239]    [Pg.549]    [Pg.139]    [Pg.530]    [Pg.114]    [Pg.176]    [Pg.352]    [Pg.353]    [Pg.290]    [Pg.170]    [Pg.21]    [Pg.180]    [Pg.17]    [Pg.137]    [Pg.172]    [Pg.137]    [Pg.138]    [Pg.131]    [Pg.74]    [Pg.199]   
See also in sourсe #XX -- [ Pg.272 ]




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